Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours

Abstract

In this work, we define a modification of a bordered construction for self-dual codes which utilises $\lambda$-circulant matrices. We provide the necessary conditions for the construction to produce self-dual codes over finite commutative Frobenius rings of characteristic 2. Using the modified construction together with the neighbour construction, we construct many binary self-dual codes of lengths 54, 68, 82 and 94 with weight enumerators that have previously not been known to exist.

arXiv admin note: substantial text overlap with arXiv:2108.09184, arXiv:2106.12355, arXiv:2102.10354

References in corpus (2)

• New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction
• A group induced four-circulant construction for self-dual codes and new extremal binary self-dual codes